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Can someone explain the difference between a GSM phone and a GSM capable phone?

I spent 45 minutes trying to comprehend the Verizon employee who seemed to be making stuff up as he went along. I told him that I want a phone that I can use in Europe and the US. He said that I need a GSM phone.

I asked him if he had any GSM phones. He said that they have Global and World Ready phones but no GSM phones, I would have to go to AT&T.

I asked if the Global and World Ready phones would work in Europe. He said that they would work ok.

I asked what he meant by "ok". He said that the phone was primarily CDMA but it had some GSM functions.

I asked him what GSM functions it was lacking. He said none.

I asked him, If it's not missing any GSM functions, then it's as good as a GSM phone, right? I'll be able to use it in Europe? He said, "Well, sort of".

And we went in circles like this for 45 minutes - I got no useful answer and left the store. I don't want to buy from AT&T but I do want to hit this Verizon employee in the face with a shovel. Not a plastic snow shovel but a solid steel ditch digging shovel.

Can some smart person here please help me lower my blood pressure by explaining what the Veriz. guy was trying to say?